special elements in a lattice
Let be a lattice and is said to be
distributive if ,
standard if , or
for all . There are also dual notions of the three types mentioned above, simply by exchanging and in the definitions. So a dually distributive element is one where for all , and a dually standard element is similarly defined. However, a dually neutral element is the same as a neutral element.
Remarks For any , suppose is the property in such that iff and imply for all .
- 1 G. Birkhoff Lattice Theory, 3rd Edition, AMS Volume XXV, (1967).
- 2 G. Grätzer, General Lattice Theory, 2nd Edition, Birkhäuser (1998).
|Title||special elements in a lattice|
|Date of creation||2013-03-22 16:42:29|
|Last modified on||2013-03-22 16:42:29|
|Last modified by||CWoo (3771)|